Round 378,903.97 to the nearest thousand

Answer:

Global extrema:  none.  Local extrema:  (0, 0) and (4, -32)

Step-by-step explanation:

ƒ(x) = x3 – 6x2 should be written as  ƒ(x) = x^3 – 6x^2.  Use " ^ " to denote exponentiation, please.

One way to answer this problem would be to make a careful graph of ƒ(x) = x^3 – 6x^2.  Notice that this graph begins in Quadrant III and ends in Quadrant I; this is one outcome of its being an ODD function.  The graph will increase, reach a peak (a local max), decrease, reach a valley (a local min) and then grow from then on.

Another way is to use calculus.  You don't say what course you're in, so I can't be sure that calculus would make sense to you.

Find the first derivative of  ƒ(x) = x^3 – 6x^2.  It is f '(x) = 3x^2 - 12x.  Set this derivative = to 0 and find the roots.  Hint:  find the roots of 3x^2(x - 4).  They are x = 0 and x = 4.  At x = , y = f(0) = 0.  Thus, the local max is

(0, 0).  At x = +4, y = f(4) = 64 - 6(16) = -32.  Thus, the local min is at (4, -32 ).

This graph rises without bound as x goes to ∞, and decreases without bound as x goes to -∞.  Thus, there is neither a global max nor a global min.  

Subtract the like terms:

6x^2 - 2x^2 = 4x^2

3x - -4x = 3x+4x = 7x

1 - 5 = -4

Now combine them to get the final answer:

4x^2 + 7x - 4

Answer:

Option 4 is the correct option.

Step-by-step explanation:

We need to solve the expression 2x(x+2)(x-3)

Multiplying the terms with each other we get,

[tex]2x(x+2)(x-3)\\=2x(x^2 -3x+2x-6)\\=2x(x^2 -x -6)\\=2x^3 -2x^2 -12x[/tex]

Option 4 is the correct option.

The value of c=12 will makes the equation true. for the given expression.

Here in the question we have expression:

[tex]\dfrac{3\sqrt{x^3}}{cy^4}}=\dfrac{x}{4y^3\sqrt{y}}[/tex]

By solving the above equation we will get:

[tex]12\sqrt{x}=c\sqrt{y}[/tex]

So value of c=12 will makes the equation true. for the given expression.

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The correct value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

To find the value of [tex]\( c \)[/tex], we start by simplifying the given equation:

[tex]\[ 3\sqrt{\frac{x^3}{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

First, we simplify the left side of the equation by applying the cube root to both the numerator and the denominator:

[tex]\[ \frac{3\sqrt{x^3}}{3\sqrt{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] , and the cube root of [tex]\( y^4 \)[/tex] is [tex]\( y \)[/tex] times the cube root of [tex]\( y \)[/tex], which is [tex]\( y \cdot y^{1/3} \)[/tex]. Simplifying further, we get:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

Now, we simplify the right side of the equation:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x \cdot 3\sqrt{y}}{4y} \][/tex]

Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are positive, we can multiply both sides by [tex]\( 4y \)[/tex] to eliminate the denominators:

[tex]\[ \frac{4yx}{3\sqrt{c} \cdot y} = x \cdot 3\sqrt{y} \][/tex]

Simplifying, we get:

[tex]\[ \frac{4x}{3\sqrt{c}} = 3x\sqrt{y} \][/tex]

Now, we can divide both sides by [tex]\( x \)[/tex] since [tex]\( x > 0 \)[/tex]:

[tex]\[ \frac{4}{3\sqrt{c}} = 3\sqrt{y} \][/tex]

Next, we square both sides to eliminate the square root:

[tex]\[ \left(\frac{4}{3\sqrt{c}}\right)^2 = (3\sqrt{y})^2 \][/tex]

[tex]\[ \frac{16}{9c} = 9y \][/tex]

Since [tex]\( y > 0 \)[/tex], we can multiply both sides by [tex]\( 9c \)[/tex] to get rid of the denominator:

[tex]\[ 16 = 81cy \][/tex]

Now, we divide both sides by [tex]\( y \)[/tex]:

[tex]\[ \frac{16}{y} = 81c \][/tex]

Finally, we multiply both sides by [tex]\( y \)[/tex] to solve for [tex]\( c \)[/tex]:

[tex]\[ 16 = 81c \][/tex]

[tex]\[ c = \frac{16}{81} \][/tex]

[tex]\[ c = \left(\frac{2^4}{3^4}\right) \][/tex]

[tex]\[ c = \left(\frac{2}{3}\right)^4 \][/tex]

[tex]\[ c = \left(\frac{3}{2}\right)^{-4} \][/tex]

[tex]\[ c = 64 \][/tex]

Therefore, the value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

[tex]\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x^2+15x+\boxed{?}^2\implies \stackrel{\textit{we know the middle term is}}{2\sqrt{x^2}\cdot \sqrt{\boxed{?}^2}\implies 2x\boxed{?}}\qquad then\qquad 2x\boxed{?}=15x \\\\\\ \boxed{?}=\cfrac{15x}{2x}\implies \boxed{?}=\cfrac{15}{2}\qquad \impliedby \textit{we should add that much \underline{squared}} \\\\[-0.35em] ~\dotfill\\\\ x^2+15x+\left( \cfrac{15}{2} \right)^2\implies \left(x+ \cfrac{15}{2} \right)^2[/tex]

Answer:

A. Step One

B. She multiplied straight across in the proportion instead of diagonally

Step-by-step explanation:

Answer:

A. Step One

B. She multiplied straight across in the proportion instead of diagonally

Answer:

AA

Step-by-step explanation:

we know that

The AA postulate states that two triangles are similar if they have two corresponding angles that are congruent

In the triangle JKL find the measure of angle L

Remember that in a triangle the sum of the interior angles must be equal to 180 degrees

so

∠J+∠K+∠L=180°

substitute the given values

105°+50°+∠L=180°

∠L=180°-155°=25°

Compare the measure of two corresponding angles of triangles JKL and MPN

∠J=∠M=105°

∠L=∠N=25°

therefore

The triangles JKL and MPN are similar by AA similarity postulate

Answer:

c = 25

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to find c

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

c² = 7² + 24² = 49 + 576 = 625

Take the square root of both sides

c = [tex]\sqrt{625}[/tex] = 25

Answer:

C=25

Step-by-step explanation:

Square both 24 and 7,Then add them together.

576+49=C

625=C

Square root 625

C=25

Answer:

Question 10: [tex]f(x)=1/2x-1[/tex] Question 13: [tex]f(-2)=-1[/tex] Question 11: [tex]f(8)=60[/tex]

Step-by-step explanation:

For Question 10:

The functionis in the form of [tex]f(x)[/tex]. We know the slope is [tex]\frac{1}{2}[/tex] (rise 1 run 2)and the y intercept is -1 (where the line goes through the y axis). We can then put the function is slope intercept form ([tex]y=mx+b[/tex]) and we would have [tex]f(x)=1/2x-1[/tex].

For Question 13:

To evaluate the function[tex]f(x)=\frac{3}{2} x-4[/tex] for [tex]f(-2)[/tex] we need to plug -2 into the function as x. [tex]f(-2)=\frac{3}{-2} (-2)-4[/tex]. [tex]\frac{3}{-2}[/tex] times -2 would equal 3 because the negatives cancle out. 3-4 equals -1 so the solution is [tex]f(-2)=-1[/tex].

For question 11:

Same as question 13. plug 8 into x in [tex]f(x)=x^2-4[/tex]. This would be [tex]f(8)=(8)^2-4[/tex]. 8 squared is 64 and 64-4 is 60. Therefore [tex]f(8)=60[/tex].

Answer:

x = z - w

Step-by-step explanation:

Given

w + x = z ( isolate x by subtracting w from both sides )

x = z - w

Answer:

x = z - w

Step-by-step explanation:

Take w to the other side and subtract with z to make x the subject

Answer:

3x^2+6x+4 is the answer :D

The sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given polynomials:

= (6x + 7 + x²) + (2x² - 3)

To add the polynomials, we must add the like terms:

= 3x² + 6x +4

Thus, the sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.

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Answer:

Step-by-step explanation:

so wa

Step-by-step explanation:

3- -5 equals 8. 8/2 equals 4. 4 plus -5=-1. so the x coordinate=-1.

2- -7=5. 5/2=2.5. 2.5+-5=2.5. so the y coordinate= 2.5. so the full set of coordinates= -1,-2.5

Answer:

7.8 rounded to the nearest whole number would be 8.

Step-by-step explanation:

-6 would be x1

7 would be y1

-1 would be x2

1 would be y2

Take these numbers and plug them into the distance formula:

[tex]\sqrt{(x2-x1)^{2}  + (y2-y1)^2}[/tex]

[tex]\sqrt{(-1 - -6)^2 + (1-7)^2} \\\sqrt{(5)^2 + (6)^2\\\} \\\sqrt{25 + 36} \\\sqrt{61} = 7.81[/tex]

Answer:

(fºg)(x) = [tex]6x^{4}+9[/tex]

Step-by-step explanation:

We have been given the following two functions;

f(x) = 6x + 9

g(x) = X^4,

We are then required to determine the expression for (fºg)(x). (fºg)(x) denotes a composite function f[g(x)] which is obtained by

substitute g(x)  in place of x in f(x)

(fºg)(x) =  6[g(x)] + 9

(fºg)(x) = 6X^4 + 9

Answer:

B

Step-by-step explanation:

3,2

9,6

(6-2)/(9-3)

Answer:

The answer is B

Step-by-step explanation:

6-2

9-3

=

12-6

8-9

Answer:

Coordinates of A': will NOT be the same

Coordinates of C': will NOT be the same

Perimeter of ABC: will be the same

Area of A'B'C': will be the same

Measure of ∠B: will be the same

Slope of A'C': will be the same

Step-by-step explanation:

We have a triangle ABC that will be translated (moved) 2 units down, 3 units to the right.

Since the triangle is moved, then the coordinates of every summit (A, B and C) will be affected.  So,

Coordinates of A': will NOT be the same

Coordinates of C': will NOT be the same

However, since the triangle is only moved, not transformed in any way, not scaled up/down for example the following will remain the same:

Perimeter of ABC: will be the same

Area of A'B'C': will be the same

Measure of ∠B: will be the same

Since the triangle is only translated, not rotated or reflected the following will remain the same:

Slope of A'C': will be the same

Hello there!

The answer is the first option.

Remember that congruent = same size and same shape, and this is the only option that has both of those things. In the second and forth options, the sizes are different making those options not correct. In the 3rd option, the shape is slightly different since one triangle is not as stretched out as the other.

I hope this was helpful and have a great day!

Since the two sides and one angle in figure 1 are the same as a result they are congruent.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

While the similarity law for triangles is defined as the law to prove that two triangles have the same shape, it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Thus, the two sides and one angle in figure 1 are the same as a result they are congruent.

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Answer:

£210

Step-by-step explanation:

A decrease of 30% represents 70% of the original cost.

100% represents the original cost

Divide the price by 70 to find 1% then multiply by 100 for original cost

original cost = [tex]\frac{147}{70}[/tex] × 100 = 2.1 × 100 = £210

Answer:

210

Step-by-step explanation:

let original price =x

x×70÷100=147

x=147×100÷70=210

ANSWER

A. (8)(-4.5)

EXPLANATION

The given expression is

[tex] - 4.5 \times - 8[/tex]

We evaluate this to obtain:

[tex]- 4.5 \times - 8 = 36[/tex]

For option A

[tex](8) \times - 4.5 = - 36[/tex]

For option B

[tex]8 \times 4.5 = 36[/tex]

For option C,

[tex] - 8 \times - 4.5 = 36[/tex]

For option D

[tex](4.5)(8) = 36[/tex]

The odd one is option A.

The correct answer is A.

A because it would become negative while the rest become positive.

Answer:

Second degree trinomial.

Step-by-step explanation:

Answer:

the opposite sides are of equal length; - the diagonals bisect each other; - the opposite angles are congruent; - the sum of any two consecutive angles is equal to 180 . Rhombis (plural of rhombus) have additional properties. Theorem 1. In a rhombus, the diagonals are the angle bisectors.

Step-by-step explanation:

The diagonals of a rhombus bisect opposite interior angles because they create congruent triangles that have equal corresponding angles.

The question addresses a geometry concept about the properties of a rhombus. To justify that the diagonals of a rhombus bisect opposite interior angles, we can consider the definition of a rhombus as a special type of parallelogram where all four sides are of equal length. Additionally, we know that in a parallelogram, opposite sides are parallel. By drawing the diagonals of a rhombus, we create congruent triangles because of the properties of parallelograms and the fact that all sides of a rhombus are equal. Each diagonal will bisect the angle from which it is drawn because in these congruent triangles, the corresponding angles are equal. This means that the diagonals bisect each other and they bisect the opposite interior angles into equal parts.

Just by itself? No it is not.

Answer:

+14.9%

Step-by-step explanation:

From 74 to 85 hours is a positive change of 11 (an increase).

Calculate 11/74:  It is 0.1486.

Multiplying this by 100% yields 14.9%.

The increase from 74 hours to 85 hours is 14.9% in magnitude.

Answer:

From 74 hours to 85 hours is approximately 15%. It is an increase.

Step-by-step explanation:

Subtract 85-74 and it'll be 11. From there, divide 11 by 74 and you'll get 0.1486... . Move the decimal place two space to the right and round the 8 to the nearest whole number. Since 8 is greater than 5, you will then round it to 15%.

M<2=105. They must add up to 180.

Step-by-step explanation:

Let's say x is the amount of $2.70/lb coffee and y is the amount of $3.20/lb coffee.

The total amount is:

x + y = 400

The total worth is:

2.70x + 3.20y = 3.00×400

2.7x + 3.2y = 1200

Solving the system of equations through substitution:

x = 400 - y

2.7 (400 - y) + 3.2y = 1200

1080 - 2.7y + 3.2y = 1200

0.5y = 120

y = 240

x = 160

The grocer uses 160 pounds of the $2.70/lb coffee and 240 pounds of the $3.20/lb coffee.

By solving a system of equations, we will see that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.

First, we need to define the variables, we can use:

We know that they make 400 pounds of the mixture, then:

x + y = 400

We also know that the price of the mixture is $3.00 per pound, then we will have that:

x*$2.70 + y*$3.20 = 400*$3.00

So the system of equations is:

x + y = 400

x*$2.70 + y*$3.20 = 400*$3.00

To solve this, we isolate one of the variables in one of the equations. For example, I will isolate x on the first equation:

x = 400 - y

Now we can replace that on the other equation to get:

(400 - y)*$2.70 + y*$3.20 = 400*$3.00

And solve this for y.

400*$2.70 - y*$2.70 + y*$3.20 = 400*$3.00

y*$0.50 = 400*$3.00 - 400*$2.70 = 400*$0.30

y = ( 400*$0.30)/$0.50 = 240

Then we have:

x = 400 - y = 400 - 240 = 160

This means that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.

If you want to learn more about systems of equations, you can read:

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Answer:

24.2%

Explanation:

The percentage of people choosing strawberry can be calculated as follows:

[tex]Percentage = \frac{PeopleChoosingStrawberry}{TotalNumberOfSurveyedPeople} * 100[/tex]

We have:

Number of people choosing strawberry = 15 people

Total number of surveyed people = 17 + 10 + 17 + 3 + 15 = 62 people

Substitute in the above rule to get the percentage as follows:

[tex]Percentage = \frac{15}{62}*100 = 24.19 = 24.2[/tex]%

Hope this helps :)

ANSWER

A.

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

EXPLANATION

Given

[tex]f(x) = \frac{x + 3}{4} [/tex]

Let

[tex]y= \frac{x + 3}{4} [/tex]

Interchange x and y

[tex]x= \frac{y + 3}{4} [/tex]

Solve for y,

[tex]4x = y + 3[/tex]

y=4x-3

This implies that,

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

Answer:

sinA=15/17 and cosA=8/17

Step-by-step explanation:

sine is opposite side over hypotenuse and cosine is adjacent side over hypotenuse

Answer:

sin A = [tex]\frac{15} {17} [/tex] and cos A =[tex] \frac{8}{17}[/tex]

Step-by-step explanation:

We are given a right angled triangle and we are to determine the ratios for sin A and cos A.

Sin is the ratio of perpendicular/hypotenuse while cos is the ratio of base/hypotenuse.

With respect to angle A, base = 8, perpendicular = 15 and hypotenuse = 17.

Therefore, [tex]sin A = \frac{15}{17}[/tex] and [tex]cos A = \frac{8}{17}[/tex].

Answer: $72.30

Step-by-step explanation:

[tex]I=P*r*t[/tex]

P is the principal amount, $482.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 3 years

The answer you're looking for is $72.30. To find this answer multiply $482 by 0.05 (five percent). From there you'll get 24.1, then multiply that by 3 (three years), and you'll get $72.30/ Hope that helps! :)